Affine Pricing and Hedging of Collateralized Debt Obligations

TL;DR

This paper develops an affine two-factor model with a catastrophic risk component for pricing and hedging single-tranche CDOs, demonstrating its effectiveness for mezzanine tranches through empirical and simulation analyses.

Contribution

It introduces a novel affine two-factor model with catastrophic risk, and derives a variance-minimizing hedging strategy for STCDOs, validated with real data and simulations.

Findings

Variance-minimizing hedge performs well for mezzanine tranches.

Hedging strategy is less effective for equity tranches.

Model captures super-senior tranche dynamics due to catastrophic component.

Abstract

This study deals with the pricing and hedging of single-tranche collateralized debt obligations (STCDOs). We specify an affine two-factor model in which a catastrophic risk component is incorporated. Apart from being analytically tractable, this model has the feature that it captures the dynamics of super-senior tranches, thanks to the catastrophic component. We estimate the factor model based on the iTraxx Europe data with six tranches and four different maturities, using a quasi-maximum likelihood (QML) approach in conjunction with the Kalman filter. We derive the model-based variance-minimizing strategy for the hedging of STCDOs with a dynamically rebalanced portfolio on the underlying swap index. We analyze the actual performance of the variance-minimizing hedge on the iTraxx Europe data. In order to assess the hedging performance further, we run a simulation analysis where normal and extreme loss scenarios are generated via the method of importance sampling. Both in-sample hedging and simulation analysis suggest that the variance-minimizing strategy is most effective for mezzanine tranches in terms of yielding less riskier hedging portfolios and it fails to provide adequate hedge performance regarding equity tranches.